Recent tensor network techniques for simulating system-environment wave functions have provided profound insights into non-Markovian dissipation and decoherence in open quantum systems. Here, we propose a dynamically adaptive one-site time-dependent-variational-principle (A1TDVP) method for matrix product states in which local bond dimensions grow to capture developing system-bath entanglement. This avoids the need for multiple convergence runs with respect to bond dimensions and the unfavorable local Hilbert space scaling of two-site methods. A1TDVP is thus ideally suited for open quantum dynamics in finite-temperature bosonic environments, as the initial states typically have low bond dimension but require very large local physical dimensions. We demonstrate this with simulations of nonequilibrium heat flows through a qubit spin, finding a $30\times$ and $10\times$ speed-up over 2TDVP and 1TDVP, respectively.

中文翻译：

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使用矩阵乘积状态的单点时间相关变分原理的有限温度开放量子动力学的有效键自适应方法

最近用于模拟系统-环境波函数的张量网络技术为开放量子系统中的非马尔可夫耗散和退相干提供了深刻的见解。在这里，我们提出了一种动态自适应单点时间相关变分原理 (A1TDVP) 方法，用于矩阵乘积状态，其中局部键尺寸增长以捕获发展中的系统浴纠缠。这避免了关于键尺寸和不利的局部希尔伯特空间缩放的双站点方法的多次收敛运行的需要。因此，A1TDVP 非常适合有限温度玻色子环境中的开放量子动力学，因为初始状态通常具有低键维但需要非常大的局部物理维。我们通过模拟非平衡热流通过量子位自旋来证明这一点，找到一个$30\times$ 和 $10\times$ 分别比 2TDVP 和 1TDVP 加速。